Covariant Theory of Gravitation in the Spacetime with Finsler Structure

TL;DR

This paper develops a covariant gravitational theory within Finsler spacetime, extending Einstein's general relativity to a broader geometric framework while maintaining covariance.

Contribution

It introduces a covariant gravitation theory in Finsler spacetime that generalizes Einstein's relativity and reduces to it in the Riemannian limit.

Findings

The theory maintains general covariance.

It reduces to Einstein's general relativity in Riemannian cases.

Provides a geometric foundation for gravitation in Finsler spacetime.

Abstract

The theory of gravitation in the spacetime with Finsler structure is constructed. It is shown that the theory keeps general covariance. Such theory reduces to Einstein's general relativity when the Finsler structure is Riemannian. Therefore, this covariant theory of gravitation is an elegant realization of Einstein's thoughts on gravitation in the spacetime with Finsler structure.